3/31/2015 12:20 AM PT

EXCLUSIVE

"Jerry Springer" producer Jill Blackstone did not carry out her sister's wish to end her life -- she murdered her ... at least that's what law enforcement now believes.

Our law enforcement sources say Wendy Blackstone -- who was deaf and partially blind -- did not want to end her life. During the initial stage of the investigation we're told cops thought this might have been a double suicide plan where Jill backed out at the last minute, but now they believe it's simple murder.

TMZ broke the story ... Wendy was found dead in their garage and Jill had severe carbon monoxide poisoning from a lit barbecue in their closed garage. We're now told in addition to the coals under the grill, there was a metal trash can filled with charcoal which had also burned.

Cops determined early on ... the suicide note found in Wendy's hand was not written by her ... they believe Jill wrote it.

Blackstone was arrested for murder earlier this month but the D.A. felt there wasn't enough evidence to make a case, so prosecutors sent it back to the LAPD for further investigation. In the meantime, Jill remains free.

But now we're told ... after more probing, the cops firmly believe it was murder.